I upgraded from Xiaomi 12 Eu to Xiaomi 13 Eu via fastboot.
When you install Xiaomi Eu for the first time from the original Xiaomi rom, you must lose all your data (it is mandatory). After you install twrp and you will want to install the Xiaomi Eu update you don't have to erise your data anymore.
Take a look here:
How to install a xiaomi.eu recovery image Because of more and more working TWRP or OrangeFox on MIUI13 Android12 a little How To and here we go .... Unlock your device (only once) - you need to unlock bootloader -> a small [howto] to unlock bootloader Install Tools and Drivers - install USB...
xiaomi.eu
It's explained very well.